共查询到20条相似文献,搜索用时 31 毫秒
1.
Manel Sanchón 《Potential Analysis》2007,27(3):217-224
We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u
* belongs to L
∞ (Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)).
This work was partially supported by MCyT BMF 2002-04613-CO3-02. 相似文献
2.
We prove a mean value inequality for non-negative solutions to in any domain Ω ⊂ ℝ
n
, where is the Monge–Ampère operator linearized at a convex function ϕ, under minimal assumptions on the Monge–Ampère measure of ϕ. An application to the Harnack inequality for affine maximal hypersurfaces is included.
相似文献
3.
Abdelmajid Siai 《Potential Analysis》2006,24(1):15-45
Let Ω be an open bounded set in ℝN, N≥3, with connected Lipschitz boundary ∂Ω and let a(x,ξ) be an operator of Leray–Lions type (a(⋅,∇u) is of the same type as the operator |∇u|p−2∇u, 1<p<N). If τ is the trace operator on ∂Ω, [φ] the jump across ∂Ω of a function φ defined on both sides of ∂Ω, the normal derivative
∂/∂νa related to the operator a is defined in some sense as 〈a(⋅,∇u),ν〉, the inner product in ℝN, of the trace of a(⋅,∇u) on ∂Ω with the outward normal vector field ν on ∂Ω. If β and γ are two nondecreasing continuous real functions everywhere
defined in ℝ, with β(0)=γ(0)=0, f∈L1(ℝN), g∈L1(∂Ω), we prove the existence and the uniqueness of an entropy solution u for the following problem,
in the sense that, if Tk(r)=max {−k,min (r,k)}, k>0, r∈ℝ, ∇u is the gradient by means of truncation (∇u=DTku on the set {|u|<k}) and
, u measurable; DTk(u)∈Lp(ℝN), k>0}, then
and u satisfies,
for every k>0 and every
.
Mathematics Subject Classifications (2000) 35J65, 35J70, 47J05. 相似文献
4.
Let A be a compact set in of Hausdorff dimension d. For s ∈ (0,d) the Riesz s-equilibrium measure μ
s
is the unique Borel probability measure with support in A that minimizes
over all such probability measures. If A is strongly -rectifiable, then μ
s
converges in the weak-star topology to normalized d-dimensional Hausdorff measure restricted to A as s approaches d from below.
This research was supported, in part, by the U. S. National Science Foundation under grants DMS-0505756 and DMS-0808093. 相似文献
5.
Our aim is to construct new examples of totally ordered and ∗-ordered noncommutative integral domains. We will discuss the
following classes of rings: enveloping algebras U(L), group rings
G and smash products U(L)
G. All of them are examples of Hopf algebras. Characterizations of orderability for enveloping algebras and group rings and
of ∗-orderability for enveloping algebras have been found before and will be recalled in the article. Our main results are:
for and L finite–dimensional, we characterize the orderability of U(L)
G; for , we give a necessary and a sufficient condition for ∗-orderability of
G (G orderable, respectively, G residually ‘torsion-free nilpotent’). Moreover, for and L finite-dimensional, we reduce the problem of characterizing the ∗-orderability of U(L)
G to the problem of characterizing the ∗-orderability of
G. The latter remains open.
The research of the first author was supported by the Ministry of Education, Science and Sport of the Republic of Slovenia
under grant P1-0222 (Algebraic methods in operator theory). The research of the second and third author was supported by the
Natural Sciences and Engineering Research Council of Canada. 相似文献
6.
Let be a bounded domain with C
2 boundary. And let H
k
be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H
k
for which the mixed-norm ||·||
p, q, ϕ
<∞. The main result of the paper is the norm equivalence:
where x
0 is a fixed point in Ω, m is a positive integer and is the jth gradient of f. A similar result for Bloch-type spaces is also obtained.
This research is partially supported by the National Natural Science Foundation of China (10471039), the MNZŽS Grant No. 144010
(Serbia), and the Natural Science Foundation of Zhejiang Province (M103104). 相似文献
7.
Norbert Hegyvári 《The Ramanujan Journal》2009,19(1):1-8
We investigate additive-multiplicative bases in
. Let
, s>2, and
. It is proved that
, provided min {|B|
s/2|A|(s−2)/2,|A|
s/2|B|(s−2)/2}>p
s/2.
This note is supported by “Balaton Program Project” and OTKA grants K 61908, K 67676. 相似文献
8.
In this paper, we study a Green’s functions G
E
, G
S
for an elasto-static equations and Stokes equations in a three-dimensional bounded Lipschitz domain Ω. We prove that there
is a positive constant c > 0 depending on the Lipschitz constant such that for all . Furthermore, we show that there is a positive constant η ∈ (0,1) depending on the Lipschitz constant such that for all .
The second author is partially supported by Korea Research Foundation Grant KRF C-00005. 相似文献
9.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
10.
Ilwoo Cho 《Acta Appl Math》2007,95(2):95-134
In this paper, we will define a graph von Neumann algebra over a fixed von Neumann algebra M, where G is a countable directed graph, by a crossed product algebra = M ×
α
, where is the graph groupoid of G and α is the graph-representation. After defining a certain conditional expectation from onto its M-diagonal subalgebra we can see that this crossed product algebra is *-isomorphic to an amalgamated free product
where = vN(M ×
α
where is the subset of consisting of all reduced words in {e, e
–1} and M ×
α
is a W
*-subalgebra of as a new graph von Neumann algebra induced by a graph G
e
. Also, we will show that, as a Banach space, a graph von Neumann algebra is isomorphic to a Banach space ⊕
where is a certain subset of the set E(G)* of all words in the edge set E(G) of G.
The author really appreciates to Prof F. Radulescu and Prof P. Jorgensen for the valuable discussion and kind advice. Also,
he appreciates all supports from St. Ambrose Univ.. In particular, he thanks to Prof T. Anderson and Prof V. Vega for the
useful conversations and suggestions. 相似文献
11.
Andrzej Komisarski 《Journal of Theoretical Probability》2008,21(4):812-823
For a probability space (Ω,ℱ,P) and two sub-σ-fields
we consider two natural distances:
and
. We investigate basic properties of these distances. In particular we show that if a distance (ρ or
) from ℬ to
is small then there exists Z∈ℱ with small P(Z), such that for every B∈ℬ there exists
such that B∖Z and A∖Z differ by a set of probability zero. This improves results of Neveu (Ann. Math. Stat. 43(4):1369–1371, [1972]), Jajte and Paszkiewicz (Probab. Math. Stat. 19(1):181–201, [1999]).
相似文献
12.
Given an open set in , we prove that every function in is zero everywhere on the boundary if and only if is regular in capacity. If in addition is bounded, then it is regular in capacity if and only if the mapping from into is injective, where denotes the Perron solution of the Dirichlet problem. Let be the set of all open subsets of which are regular in capacity. Then one can define metrics and on only involving the resolvent of the Dirichlet Laplacian. Convergence in those metrics will be defined to be the local/global uniform convergence of the resolvent of the Dirichlet Laplacian applied to the constant function . We prove that the spaces and are complete and contain the set of all open sets which are regular in the sense of Wiener (or Dirichlet regular) as a closed subset. 相似文献
13.
Let (X
t
)
t⩾0 be the n-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space having the Laplace–Beltrami operator as its generator. The aim of the paper is to derive the formulas for the Gegenbauer
transform of the Poisson kernel and the Green function of the ball for the process (X
t
)
t⩾0. Under additional hypotheses we prove integral representations for the Poisson kernel. This yields explicit formulas in and spaces for the Poisson kernel and the Green function as well.
相似文献
14.
Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure
μ
T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace
affiliated with ℳ, such that the Brown measure of
is concentrated on B and the Brown measure of
is concentrated on ℂ∖B. Moreover,
is T-hyperinvariant and the trace of
is equal to μ
T(B). In particular, if T∈ℳ has a Brown measure which is not concentrated on a singleton, then there exists a non-trivial, closed,
T-hyperinvariant subspace. Furthermore, it is shown that for every T∈ℳ the limit
exists in the strong operator topology, and the projection onto
is equal to 1[0,r](A), for every r>0.
Supported by The Danish National Research Foundation. 相似文献
15.
Let B
H
and
be two independent, d-dimensional fractional Brownian motions with Hurst parameter H∈(0,1). Assume d≥2. We prove that the intersection local time of B
H
and
exists in L
2 if and only if Hd<2.
相似文献
16.
In the study of the asymptotic behaviour of solutions of differential-difference equations the
-spectrum has been useful, where
and
implies Fourier transform
, with
given
, φ∈L
∞(ℝ,X), X a Banach space,
(half)line. Here we study
and related concepts, give relations between them, especially
weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =
; also
= Beurling spectrum of “φ modulo
” (Chill-Fasangova). If
satisfies a Loomis type condition (L
U
), then
countable and
uniformly continuous ∈U are shown to imply
; here (L
U
) usually means
, indefinite integral Pf of f in U imply Pf in
(the Bohl-Bohr theorem for
= almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes
, ℳ
m
U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with
in some
we show
. With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral
integro-differential-difference systems. Also many examples and special cases are discussed. 相似文献
17.
18.
A frame homomorphism h : A ⟶ B is skeletal if x
⊥⊥ = 1 in A implies that h(x)⊥⊥ = 1 in B. It is shown that, in , the category of compact regular frames with skeletal maps, the subcategory , consisting of the frames in which every polar is complemented, coincides with the epicomplete objects in . Further, is the least epireflective subcategory, and, indeed, the target of the monoreflection which assigns to a compact regular
frame A, the ideal frame ε A of , the boolean algebra of polars of A.
相似文献
19.
Our main result is that the simple Lie group G = Sp(n, 1) acts metrically properly isometrically on L
p
(G) if p > 4n + 2. To prove this, we introduce Property , with V being a Banach space: a locally compact group G has Property if every affine isometric action of G on V, such that the linear part is a C
0-representation of G, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic
groups over a local field of characteristic zero, have Property . As a consequence, for unitary representations, we characterize those groups in the latter classes for which the first cohomology
with respect to the left regular representation on L
2(G) is nonzero; and we characterize uniform lattices in those groups for which the first L2-Betti number is nonzero.
相似文献
20.
Sangwook Kim 《Discrete and Computational Geometry》2008,40(2):190-213
We prove that if a simplicial complex Δ is shellable, then the intersection lattice L
Δ for the corresponding diagonal arrangement
is homotopy equivalent to a wedge of spheres. Furthermore, we describe precisely the spheres in the wedge, based on the data
of shelling. Also, we give some examples of diagonal arrangements
where the complement
is K(π,1), coming from rank-3 matroids.
This work forms part of the author’s doctoral dissertation at the University of Minnesota, supervised by Vic Reiner, and partially
supported by NSF grant DMS-0245379. 相似文献